Early Numeracy Intervention Grade 1
Study: Bryant et al. (2011)

Describe how students were selected to participate in the study:

All students in first grade in 10 elementary schools in the same school district who had parent consent and assent were selected to participate in the study.

Describe how students were identified as being at risk for academic failure (AI) or as having emotional or behavioral difficulties (BI):

Two main considerations drove sample selection: (a) maintaining sufficient power and (b) reliably assessing risk. Of the initial pool of students (N = 771), the lowest 35% (n = 269) was identified as being “at-risk” based on an initial administration of the Texas Early Mathematics Inventories-Progress Monitoring measures (TEMI-PM; University of Texas System & Texas Education Agency, 2007a; refer to the Measures for further details about this test) in the fall (September). Students were administered four additional TEMI-PM probes (alternate forms of the original measure used for student selection) over a 3-week period to determine whether there were false positives among the initial pool of students. False positives are a particular concern given the generally “chaotic” nature of early achievement and the increased possibility of falsely identifying students as being “at-risk” when they were merely distracted, anxious, or unfamiliar with the testing protocols. Growth modeling (with continuous outcomes and auto-correlated residuals) was used to estimate case-level factor scores for intercept and slope for each of the 238 cases using PLUS 4.1 (preliminary analyses suggested a statistically significant positive trend in scores over time, on average thus, a growth model approach was preferred over a confirmatory factor model). Intercept was conceptualized as the last of the four additional TEMI-PM measures (beyond the TEMI-PM used to initially identify the lowest 35%). Estimated time 4 scores were used to make final sample selection. The cut score was selected based on the probabilities of diagnostic accuracy (i.e., likelihood ratio [LR]) derived using receiver operator curve (ROC) analysis. Using this procedure, 14 students were found to be false positives and were eliminated from the sample. A concern with accuracy and the need to maintain an adequate sample size both influenced our sampling strategy. Preliminary power analyses suggested a sample size of 240, with 160 in the treatment condition and 80 in the comparison group. The initial pool of eligible students was only 238, so our strategy was to identify students who clearly were not at risk, based on their estimated score at time 4 and a very conservative risk threshold (LR: negative of 0.70). The final sample (n = 224:151 treatment and 73 control) identified for treatment and control conditions was associated with a minimal detectable effect size of approximately 0.40, assuming 0.80 power and 45 instructional groups with five students in each group.

ACADEMIC INTERVENTION: What percentage of participants were at risk, as measured by one or more of the following criteria:

• below the 30th percentile on local or national norm, or
• identified disability related to the focus of the intervention?

%

BEHAVIORAL INTERVENTION: What percentage of participants were at risk, as measured by one or more of the following criteria:

• emotional disability label,
• placed in an alternative school/classroom,
• non-responsive to Tiers 1 and 2, or
• designation of severe problem behaviors on a validated scale or through observation?

%

Specify which condition is the submitted intervention:

Early Numeracy Intervention Grade 1

Specify which condition is the control condition:

If you have a third, competing condition, in addition to your control and intervention condition, identify what the competing condition is (data from this competing condition will not be used):

Using the tables that follow, provide data demonstrating comparability of the program group and control group in terms of demographics.

Grade Level

Race–Ethnicity

Socioeconomic Status

Disability Status

ELL Status

Gender

What method was used to determine students' placement in treatment/control groups?

Random

Please describe the assignment method or the process for defining treatment/comparison groups.

Simple random assignment of students to condition was completed using a random number generator in Statistical Analysis Software.

What was the unit of assignment?

Students

If other, please specify:

Please describe the unit of assignment:

What unit(s) were used for primary data analysis?

Schools
Teachers
Students
Classes
Other
If other, please specify:

Please describe the unit(s) used for primary data analysis:

How was the program delivered?

Individually
Small Group
Classroom

What were the background, experience, training, and ongoing support of the instructors or interventionists?

The research team included two full- time intervention coordinators and five graduate research assistants (GRAs) who were doctoral and master’s students in the Department of Special Education; all of the GRAs held teaching credentials or were completing a teaching certification program. This research team was also responsible for conducting the intervention. At the beginning of the academic year, the principal investigator provided a 3-hour training on the intervention lessons and accompanying instructional materials. This training consisted of an explanation of the content and review and modeling of systematic instruction. Following this training, the research team practiced the lessons with one another. Prior to intervention, the tutors taught a lesson and received feedback from experienced tutors who were using the same lessons with a group of students. Throughout the school year, training sessions were conducted before each intervention unit (seven total sessions). Tutors were visited weekly and team meetings were held to solve issues.

Describe when and how fidelity of treatment information was obtained.

Each tutor was observed by research staff for three sessions during the 19-week intervention to assess the quality (i.e., fidelity) of specific implementation performance indicators. Quality of Implementation (QoI) indicators included the degree to which tutors (a) followed the scripted lessons (e.g., modeling, guided practice, independent practice); (b) implemented the features of explicit, systematic instruction (e.g., pacing, error correction); (c) managed student behavior (e.g., use of reinforcers and redirection); and (d) managed the lesson (e.g., use of timer, smooth transitions between booster lessons).

What were the results on the fidelity-of-treatment implementation measure?

Performance indicators were rated on a 0-to-3 point scale, in which 0 = Not at All, 1 = Rarely, 2 = Some of the Time, and 3 = Most of the Time. Results were shared with the tutors and areas in need of further training and recommendations for improved performance were discussed. Results on the QoI showed average ratings exceeding 2.5 in all areas, with no single rating of <2.0. The majority of ratings were 3.0. These results across tutors show that there was a high degree of fidelity in the implementation of the booster lessons.

Was the fidelity measure also used in control classrooms?

Yes

For any substantively (e.g., effect size ≥ 0.25 for pretest or demographic differences) or statistically significant (e.g., p < 0.05) pretest differences, please describe the extent to which these differences are related to the impact of the treatment. For example, if analyses were conducted to determine that outcomes from this study are due to the intervention and not pretest characteristics, please describe the results of those analyses here.

Please explain any missing data or instances of measures with incomplete pre- or post-test data.

If you have excluded a variable or data that are reported in the study being submitted, explain the rationale for exclusion:

Describe the analyses used to determine whether the intervention produced changes in student outcomes:

A series of analyses of covariance (ANCOVA) with the TEMI-PM Fall Total Score as the covariate was used to evaluate statistical differences between groups and to maximize power of the design. The increased Type I error rate associated with multiple comparisons was addressed using the Benjamani-Hochberg (1995) correction, which controls for false discovery rate. Two procedures were conducted, one to evaluate statistical significance of the eight non-composite scores (i.e., TEMI-PM: MC, NS, PV, and ASC; SAT-10: MPS and MP; TEMI-O: computation and problem solving) and the other to evaluate group difference on the composite scores of the TEMI-PM Total Score, TEMI-O Total Score, and SAT-10 Total Score (because composite scores are the sum of two or more non-composite measures, the procedures were separated to maintain independence of observations). Benjamani-Hochberg does not produce a new p-value. Instead, it indicates whether a given finding is significant at the specified level after correcting for multiple comparisons according to pi’= i/M, where i is the rank of pi, the original p-value, M is the total number of findings within the domain, and  is the target p-value. Assumptions regarding homogeneity of regression were evaluated for all outcomes. There were no violations. We calculated Hedges g (g*) for small sample sizes using the covariate adjusted posttest mean difference standardized with unadjusted pooled with-in groups standard deviation (Hedges & Olkin, 1985).